| Autor: |
Padoan, Simone A., Rizzelli, Stefano |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
J. Appl. Probab. 61 (2024) 529-539 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1017/jpr.2023.53 |
| Popis: |
Extreme Value Theory plays an important role to provide approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the {generalised Pareto distribution} $H_\gamma(x)$ as an approximation of the distribution $F_t(s(t)x)$ of the excesses over a threshold $t$, where $s(t)$ is a suitable norming function. In this paper we study the rate of convergence of $F_t(s(t)\cdot)$ to $H_\gamma$ in variational and Hellinger distances and translate it into that regarding the Kullback-Leibler divergence between the respective densities. |
| Databáze: |
arXiv |
| Externí odkaz: |
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